Volume 51, Number 3, May-June 2017
|Page(s)||825 - 849|
|Published online||30 March 2017|
Finite element approximation of Dirichlet control using boundary penalty method for unsteady Navier–Stokes equations
Department of Mathematical Sciences, SST 201M, The University of Alabama in Huntsville, Huntsville, AL 35899, USA.
Received: 19 February 2016
Revised: 24 May 2016
Accepted: 25 May 2016
This paper is concerned with the analysis of the finite element approximations of Dirichlet control problem using boundary penalty method for unsteady Navier–Stokes equations. Boundary penalty method has been used as a computationally convenient approach alternative to Dirichlet boundary control problems governed by Navier−Stokes equations due to its variational properties. Analysis of the mixed Galerkin finite element method applied to the spatial semi-discretization of the optimality system, from which optimal control can be computed, is presented. An optimal L∞(L2) error estimate of the numerical approximations of the optimality system is derived. Feasibility and applicability of the approach are illustrated by numerically solving a canonical flow control problem.
Mathematics Subject Classification: 65M12 / 93C20 / 76B75 / 49J20 / 65M60 / 93B40 / 76D05
Key words: Boundary penalty method / Dirichlet boundary control / Navier–Stokes equations / optimal error estimates / mixed Galerkin finite element / adjoint equations
© EDP Sciences, SMAI 2017
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